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fenix001 [56]
1 year ago
10

What is the solution to the compound inequality in interval notation?

Mathematics
1 answer:
ollegr [7]1 year ago
4 0

Answer:

Step-by-step explanation:

Because of the word "or", this is a disjunction, or a union of all the solutions to the inequality as they present on a number line.

For the first inequality:

4(x + 1) > -4 we distribute through the parenthesis to get

4x + 4 > -4 and subtract 4 from both sides to get

4x > -8 and then divide both sides by 4 to get

x > -2.  That will be graphed on a number line with an open hole over the -2 and the arrow will go to the right where the numbers are bigger than -2. This arrow continues into positive infinity.

For the other inequality:

2x - 4 ≤ -10 we add 4 to both sides to get

2x ≤ -6 and then divide by 2 to get

x ≤ -3. That is a closed hole over -3 and the arrow goes to negative infinity (to the left). Since one arrow goes off to the right forever, and the other arrow goes off to the left forever, and the arrows do not intersect at any point, the interval notation answer is

(-∞, -3] or (-2, ∞).  The parenthesis mean that the number following it is not included (you can't include infinity, either negative or positive, because it's not actually a number) and the brackets mean that the number following it IS included. The hole is closed over the -3 so -3 is included in the solution, where the hole over the -2 is open and is not included.

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I NEED HELP PLEASE, THANKS! :)
Afina-wow [57]

Answer:

Third option is the right choice.

Step-by-step explanation:

Manipulate the right hand side.

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Best Regards!

6 0
3 years ago
Read 2 more answers
A girrafe runs at a rate of 32 miles per hour. Which equation models the situation?
Anastasy [175]

Answer:A girrafe runs at a rate of 32 miles per hour. Which equation models the situation?

Step-by-step explanation:

4 0
3 years ago
How do you find the HCF of 15t and 6s?
earnstyle [38]

Answer:

HCF=3

Step-by-step explanation:

Factors of 15t= 3*5*t

Factors of 6s= 2*3*s

HCF= Common factors

common factor = 3

HCF=3

4 0
3 years ago
PLEASE HELP ASAP f(x) = x2 What is g(x)?
vfiekz [6]

Answer:

c. g(x) = 4x^2

Step-by-step explanation:

From a first glance, since g(x), is skinnier than f(x), meaning that it is increasing faster, so I know that I can eliminate options A & B since the coefficient on x needs to be greater than 1.

We can then look and see that g(1) = 4 as shown by the point given to us on the graph.

To find the right answer we can find g(1) for options C & D and whichever one matches the point on the graph is our correct answer. e

Option C:

once we plug in 1 for x, our equation looks like

4(1)^2.

1^2 = 1, and 4(1) = 4,

so g(1) = 4. and our point is (1,4).

This is the same as the graph so this is the CORRECT answer.

If you want to double check, you can still find g(1) for option D and verify that it is the WRONG answer.

Option D:

once we plug in 1 for x, our equation looks like

16(1)^2

1^2 = 1, and 16(1) = 16,

so g(1) = 16. and our point is (1,16).

This is different than the graph so this is the WRONG answer.

3 0
3 years ago
A building is 3 ft from an 8​-ft fence that surrounds the property. A worker wants to wash a window in the building 13 ft from t
zloy xaker [14]

Answer:

Length of the ladder used by worker = 17 feet

Step-by-step explanation:

Given:

Height of the window from the ground = 13 ft

Distance of fence from the building = 3 ft

Distance of ladder from the building = (3+8) = 11 ft

We have to find the length of the ladder.

Let the length of the ladder be 'x'

From the diagram we can also say that 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras formula:

⇒ hypotenuse\ 'x' =\sqrt{(perpendicular)^2+(base)^2}

Here base length = 11 ft

Perpendicular = 13 ft

Plugging the values:

⇒ x=\sqrt{(13)^2+(11)^2}

⇒  x=\sqrt{(169+121)}

⇒ x= \sqrt{290}

⇒ x=17.02 feet

The length of the ladder = 17 feet to its nearest tenth.

6 0
3 years ago
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